Unwrapping the Circle - education
... Ask students to use MATHOMAT shape 3 to draw a unit circle and accurately reproduce the diagram below: emphasise that each of the 12 evenly spaced points on the circumference has associated with it an arc whose length is measured from the x-axis, and an angle subtended at the centre of the circle. ( ...
... Ask students to use MATHOMAT shape 3 to draw a unit circle and accurately reproduce the diagram below: emphasise that each of the 12 evenly spaced points on the circumference has associated with it an arc whose length is measured from the x-axis, and an angle subtended at the centre of the circle. ( ...
1.4
... worked by drawing θ is standard position in quadrant III, finding r to be 5, and then using the definitions of sin θ and cos θ in terms of x, y, and r. ...
... worked by drawing θ is standard position in quadrant III, finding r to be 5, and then using the definitions of sin θ and cos θ in terms of x, y, and r. ...
HCPSS Curriculum Framework Common Core 8 Unit 4: Geometry
... b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, d ...
... b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, d ...
Document
... is greater that the measure of either of it corresponding remote interior angles. • Theorem 5.9 – If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. • Theorem 5.10 – If one angle of a triangle ...
... is greater that the measure of either of it corresponding remote interior angles. • Theorem 5.9 – If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. • Theorem 5.10 – If one angle of a triangle ...
PP Prove Angle Pair Relationships Lesson 4.6 for 1-18
... The goal of this lesson is to be able to use the properties of special pairs of angles. ...
... The goal of this lesson is to be able to use the properties of special pairs of angles. ...
chapter 9
... shape and size as the original figure. • Any isometry is either a reflection or the composition of reflections. ...
... shape and size as the original figure. • Any isometry is either a reflection or the composition of reflections. ...
Trigonometric functions
In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component). More precise definitions are detailed below. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles (often right triangles). In this use, trigonometric functions are used, for instance, in navigation, engineering, and physics. A common use in elementary physics is resolving a vector into Cartesian coordinates. The sine and cosine functions are also commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations through the year.In modern usage, there are six basic trigonometric functions, tabulated here with equations that relate them to one another. Especially with the last four, these relations are often taken as the definitions of those functions, but one can define them equally well geometrically, or by other means, and then derive these relations.